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Solved: A barge is in a rectangular lock on a freshwater
Chapter 12, Problem 84P(choose chapter or problem)
Problem 84P
A barge is in a rectangular lock on a freshwater river. The lock is 60.0 in long and 20.0 m wide, and the steel doors on each end are closed. With the barge floating in the lock, a 2.50 × 106 N load of scrap metal is put onto the barge. The metal has density 9000 kg/m3. (a) When the load of scrap metal, initially on the bank, is placed onto the barge, what vertical distance does the water in the lock rise? (b) The scrap metal is now pushed overboard into the water. Does the water level in the lock rise, fall, or remain the same? If it rises or falls, by what vertical distance does it change?
Questions & Answers
QUESTION:
Problem 84P
A barge is in a rectangular lock on a freshwater river. The lock is 60.0 in long and 20.0 m wide, and the steel doors on each end are closed. With the barge floating in the lock, a 2.50 × 106 N load of scrap metal is put onto the barge. The metal has density 9000 kg/m3. (a) When the load of scrap metal, initially on the bank, is placed onto the barge, what vertical distance does the water in the lock rise? (b) The scrap metal is now pushed overboard into the water. Does the water level in the lock rise, fall, or remain the same? If it rises or falls, by what vertical distance does it change?
ANSWER:Solution 84P
Step 1:
a) Weight of steel = 2.5 × 106 N
If steel of weight 2.5 × 106 N is displaced into the barge, it will displace an amount of water which is equal to the weight of steel.
Therefore, weight of water displaced, Wwater = 2.5 × 106 N
Density of water, dwater = 1000 kg/m3
Therefore, volume of the water displaced, Vwater = Mwater /dwater
Mass of water can be calculated using the equation, Mwater = Wwater / g
That is, Mwater = (2.5 × 106 N) / 9.8 m/s2 = 2.551 × 105 kg